Error Model for Autonomous Global Positioning Method Using Polarized Sky Light and True North Measurement Instrument

Long-distance navigation requires global positioning methods to have complete autonomy, particularly when the Global Positioning System is unavailable. Considering that bionic polarized light-based global positioning technology exhibits good autonomy, this study develops an error model for autonomous global positioning based on the polarized skylight and a true north measurement instrument, using an approach of partial derivatives. The proposed model can rapidly and accurately provide the global error distribution of a bionic positioning method under varying angular measurement errors at different times. In addition, the conditions under which the proposed error model remains valid are investigated. The results indicate that the investigation can be simplified to verify whether the denominators of four partial derivatives of an implicit function system are simultaneously non-zero. The accuracy of the proposed error model is verified through numerical simulations. The results indicate that when the deviations of the two independent variables are up to 0.0001°, the positioning error mostly remains less than 14 m. In contrast, fewer geographical locations have positioning errors approaching positive infinity. By analyzing the global error distribution, one can effectively design and optimize the parameters of the autonomous global positioning system, enhancing its reliability and stability.